Robust Nonlinear Mapping of Soil Contamination Using Support Regression

Spatial data analysis mapping and visualization is of great importance in various fields: environment, pollution, natural hazards and risks, epidemiology, spatial econometrics, etc. A basic task of spatial mapping is to make predictions based on some empirical data (measurements). A number of state-of-the-art methods can be used for the task: deterministic interpolations, methods of geostatistics: the family of kriging estimators (Deutsch and Journel, 1997), machine learning algorithms such as artificial neural networks (ANN) of different architectures, hybrid ANN-geostatistics models (Kanevski and Maignan, 2004; Kanevski et al., 1996), etc. All the methods mentioned above can be used for solving the problem of spatial data mapping. Environmental empirical data are always contaminated/corrupted by noise, and often with noise of unknown nature. That's one of the reasons why deterministic models can be inconsistent, since they treat the measurements as values of some unknown function that should be interpolated. Kriging estimators treat the measurements as the realization of some spatial randomn process. To obtain the estimation with kriging one has to model the spatial structure of the data: spatial correlation function or (semi-)variogram. This task can be complicated if there is not sufficient number of measurements and variogram is sensitive to outliers and extremes. ANN is a powerful tool, but it also suffers from the number of reasons. of a special type ? multiplayer perceptrons ? are often used as a detrending tool in hybrid (ANN+geostatistics) models (Kanevski and Maignank, 2004). Therefore, development and adaptation of the method that would be nonlinear and robust to noise in measurements, would deal with the small empirical datasets and which has solid mathematical background is of great importance. The present paper deals with such model, based on Statistical Learning Theory (SLT) - Support Vector Regression. SLT is a general mathematical framework devoted to the problem of estimation of the dependencies from empirical data (Hastie et al, 2004; Vapnik, 1998). SLT models for classification - Support Vector Machines - have shown good results on different machine learning tasks. The results of SVM classification of spatial data are also promising (Kanevski et al, 2002). The properties of SVM for regression - Support Vector Regression (SVR) are less studied. First results of the application of SVR for spatial mapping of physical quantities were obtained by the authorsin for mapping of medium porosity (Kanevski et al, 1999), and for mapping of radioactively contaminated territories (Kanevski and Canu, 2000). The present paper is devoted to further understanding of the properties of SVR model for spatial data analysis and mapping. Detailed description of the SVR theory can be found in (Cristianini and Shawe-Taylor, 2000; Smola, 1996) and basic equations for the nonlinear modeling are given in section 2. Section 3 discusses the application of SVR for spatial data mapping on the real case study - soil pollution by Cs137 radionuclide. Section 4 discusses the properties of the modelapplied to noised data or data with outliers.

Elemental (C/N ratios) and isotopic (δ15N(org), δ13C(org)) compositions of sedimentary organic matter from a high-altitude mountain lake (Meidsee, 2661 m a.s.l., Switzerland): Implications for Lateglacial and Holocene Alpine landscape evolution

The deposition of Late Pleistocene and Holocene sediments in the high-altitude lake Meidsee (located at an altitude of 2661 m a.s.l. in the Southwestern Alps) strikingly coincided with global ice-sheet and mountain-glacier decay in the Alpine forelands and the formation of perialpine lakes. Radiocarbon ages of bottom-core sediments point out (pre-) Holocene ice retreat below 2700 m a.s.l., at about 16, 13, 10, and 9 cal. kyr BP. The Meidsee sedimentary record therefore provides information about the high-altitude Alpine landscape evolution since the Late Pleistocene/Holocene deglaciation in the Swiss Southwestern Alps. Prior to 5 cal. kyr BP, the C/N ratio and the isotopic composition of sedimentary organic matter (delta N-15(org), delta C-13(org)) indicate the deposition of algal-derived organic matter with limited input of terrestrial organic matter. The early Holocene and the Holocene climatic optimum (between 7.0 and 5.5 cal. kyr BP) were characterized by low erosion (decreasing magnetic susceptibility, chi) and high content of organic matter (C-org > 13 wt.%), enriched in C-13(org) (>-18 parts per thousand) with a low C/N (similar to 10) ratio, typical of modern algal matter derived from in situ production. During the late Holocene, there was a long-term increasing contribution of terrestrial organic matter into the lake (C/N > 11), with maxima between 2.4 and 0.9 cal. kyr BP. A major environmental change took place 800 years ago, with an abrupt decrease in the relative contribution of terrestrial organic material into the lake compared with aquatic organic material which subsequently largely dominated (C/N drop from 16 to 10). Nonetheless, this event was marked by a rise in soil erosion (chi), in nutrients input (N and P contents) and in anthropogenic lead deposition, suggesting a human disturbance of Alpine ecosystems 800 years ago. Indeed, this time period coincided with the migration of the Walser Alemannic people in the region, who settled at relatively high altitude in the Southwestern Alps for farming and maintaining Alpine passes.

Soil diffuse degassing and thermal energy fluxes from the southern Lakki plain, Nisyros (Greece)

Two diffuse soil CO2 flux surveys from the southern Lakki plain show that CO2 is mainly released from the hydrothermal explosion craters. The correspondence between high CO2 fluxes and elevated soil temperatures suggests that a flux of hot hydrothermal fluids ascends towards the surface. Steam mostly condenses near the surface and the heat given off is conductively transferred to the atmosphere through the soil, accompanied by a large CO2 flux. Tt was calculated, that 68 t d(-1) of hydrothermal CO2 are released through the total surveyed area of similar to1.3 km(2) Admitting that a steam flux of 2200 t d(-1) accompanies this CO2 flux, the thermal energy released through steam condensation amounts to 58 MW.

Controls on 13C and 14C variability in soil CO2

14C dating of groundwater depends on the isotopic composition of both the solid carbonate and the soil CO2 and requires the use of 14C age correction models. To better assess the variability of the 14C activity of soil CO2 (A14Csoil-CO2) and the δ13C of soil CO2 (δ13Csoil-CO2), which are two parameters used in 14C age correction models, we studied the different processes involving carbon isotopes in the soil. The approach used experimental data from two sites in France (Fontainebleau sands and Astian sands) and a steady-state transport model. In most cases, the 14C activity (A14C) of atmospheric CO2 is directly used in the 14C age correction models as the A14Csoil-CO2. However, we demonstrate that since 1950, the evolution of the A14Csoil-CO2 reflects the competition between the fluxes of root-derived CO2 and organic matter-derived CO2. Therefore, the A14Csoil-CO2 must be used to date groundwater that is younger than 60 years old. Moreover, the δ13C of soil CO2 (δ13Csoil-CO2) showed large seasonal variations that must be taken into account in selecting the δ13Csoil-CO2 for 14C age correction models.